APPLICATIONS OF DEGREE THEORY TO LINEAR COMPLEMENTARITY-PROBLEMS

In this paper, we consider two applications of degree theory to linear complementarity problems. In the first application, we study the stab ility of an LCP at a solution point. Specifically we prove the stabili ty of an LCP corresponding to a P0-matrix at an isolated solution. Usi ng a recent degree formula due to Stewart 1991, we strengthen a stabil ity result of Gowda and Pang 1992. In the second application, we use t he same degree formula of Stewart to describe the number of solutions of LCP(M, q) when M is a negative almost N-matrix. This analysis leads to a Lipschitzian characterization of the solution map PHI: q bar arr ow pointing right SOL(M, q) corresponding to a nondegenerate negative matrix.